Question

value of sin 45/2 is
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Answer 1

Answer:

by the half of the angle we have that: sin(x/2)=±√[(1-cos x)/2]

we pick the positive sign as sin(22.5°) is greater than 0 as 22.5° is in quadrant I

with x=45°

sin(45°/2)=√[(1-cos45°)/2]

sin (22.5°)=√[(1-√2/2]=√[(2-√2)/4]=√(2-√2)/2

Answer 2

Given:

sin $\frac{45}{2}$

To find:

the evaluated value

Solution:

We know that,

$cos A=1-2sin^2 \frac{A}{2}$

then, $sin^2\frac{A}{2}=\frac{(1-cos\frac{A}{2} ) }{2}$

Now we put the value of A as 45° and we get,

$sin^2\frac{45}{2}=\frac{(1-cos\frac{45}{2} ) }{2}$

Now, we put the trigonometric values and we obtain the equation as follows,

$sin^2 \frac{45}{2}=\frac{(1-\frac{1}{\sqrt{2}})}{2}$

⇒$sin^2 \frac{45}{2}=2-\frac{\sqrt{2} }{4}$

Taking square root from both the sides, we get,

$sin\frac{45}{2}=\frac{\sqrt{(\sqrt{2}-2)}}{2}$

Hence,after evaluatingwe get the value of sin $\frac{45}{2}$ is  $sin\frac{45}{2}=\frac{\sqrt{(\sqrt{2}-2)}}{2}$.